Related papers: Utterance Selection Model of Language Change
We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…
We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
Human history leaves fingerprints in human languages. Little is known over language evolution and its study is of great importance. Here, we construct a simple stochastic model and compare its results to statistical data of real languages.…
Fluctuations of cell state, e.g., abundances of some proteins, have attracted much attention both theoretically and experimentally. The distribution of such state over cells, however, is not only a result of intracellular stochastic…
The preservation of endangered languages is a widely discussed issue nowadays. Languages represent essential cultural heritage and can provide valuable botanical, biological, and geographical information. Therefore, it is necessary to…
One of the most intriguing features of language is its constant change, with ongoing shifts in how meaning is expressed. Despite decades of research, the factors that determine how and why meanings evolve remain only partly understood.…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the…
We consider a stochastic logistic growth model involving both birth and death rates in the drift and diffusion coefficients for which extinction eventually occurs almost surely. The associated complete Fokker-Planck equation describing the…
Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the world's existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon has…
We investigate the stochastic dynamics of entities which are confined to a set of islands, between which they migrate. They are assumed to be one of two types, and in addition to migration, they also reproduce and die. Systems which fall…
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this…
A simple spatial computer simulation model was recently introduced to study the evolution of the linguistic diversity. The model considers processes of selective geographic colonization, linguistic anomalous diffusion and mutation. In the…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
One proposed mechanism of language change concerns the role played by second-language (L2) learners in situations of language contact. If sufficiently many L2 speakers are present in a speech community in relation to the number of…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
Fisher's fundamental theorem of natural selection states that the rate of change in a population's mean fitness equals its additive genetic variance in fitness. This implies that mean fitness should not decline in a constant environment,…